Networks

In the 1930s, Jacob Moreno was thinking about the “social atom” and making “sociograms” (network diagrams).

Game of Thrones data

I am a little out of the cultural loop, so I don’t have a lot of contextual knowledge, but the hottest network analysis lately is about Game of Thrones, so…

library(readr)
storm <- read_csv("stormofswords.csv")
head(storm)

## # A tibble: 6 x 3
##   Source  Target Weight
##    <chr>   <chr>  <int>
## 1  Aemon   Grenn      5
## 2  Aemon Samwell     31
## 3  Aerys   Jaime     18
## 4  Aerys  Robert      6
## 5  Aerys  Tyrion      5
## 6  Aerys   Tywin      8

Working with networks

R packages:

igraph
network
GGally (for visualization)
ggraph (for visualization)

Other ways:

Gephi
d3

Lets try igraph first

library(igraph)
library(GGally)
g <- graph.data.frame(storm)
plot(g)

Defaults are pretty ugly.

Making igraph a bit more readable

plot(g, edge.arrow.size=0.2, vertex.size=7, vertex.label.cex=0.7)

Changing the layout– circle

plot(g, edge.arrow.size=0.2, vertex.size=7, vertex.label.cex=0.7, layout=layout_in_circle)

Changing the layout – sphere

plot(g, edge.arrow.size=0.2, vertex.size=7, vertex.label.cex=0.7, layout=layout_on_sphere)

But really, we want the “random” network to be less collapsed

l <- layout_with_fr(g,niter=500)
plot(g, edge.arrow.size=0.2, vertex.size=7, vertex.label.cex=0.7, layout=l)

It can be good to save your layout separately so you don’t get a subtle variation every time you plot.

Curved edges

plot(g, edge.arrow.size=0.2, vertex.size=7, vertex.label.cex=0.7, layout=l, edge.curved=TRUE)

What about GGally?

Lots of dependencies necessary.

library(GGally)
library(network)
library(sna)
library(intergraph)
ggnet2(g, label=TRUE)

But, defaults are prettier.

Weighted edges

ggnet2(g, label=TRUE, edge.size = "Weight", edge.alpha=0.5)

AAAAA

Okay, lets do some rescaling

library(dplyr)
storm <- storm %>%
  mutate(ScaledWeight = Weight / max(Weight))
g <- graph.data.frame(storm)
ggnet2(g, label=TRUE, edge.size = "ScaledWeight", node.size = 4)

Now I think we’ve gone too far! You will have to figure out what makes sense.

ggraph

# We're going off the rails a bit here
# library(devtools)
# install_github('hadley/ggplot2')
# install_github('thomasp85/ggforce')
# install_github("thomasp85/ggraph")
library(ggraph)
ggraph(g, 'igraph',algorithm = 'kk') +
  geom_edge_fan(aes(alpha = ..index..)) + 
  geom_node_point() +
  ggforce::theme_no_axes()

Networks in d3 – the lazy way!

library(networkD3)
gd <- get.data.frame(g)
simpleNetwork(gd)

There is more to networks than just node-edge diagrams

Lots of “centralities”

Eigenvector Centrality

ec <- eigen_centrality(g)$vector
ec <- data.frame(ec)
ec$names <- rownames(ec)
ec %>%
  arrange(desc(ec)) %>%
  slice(1:10) %>%
  ggplot() + geom_bar(aes(x=reorder(names, ec), y=ec), stat="identity")

Looks like what Andre Beveridge and Jie Shan got!

Betweenness centrality

bc <- betweenness.estimate(g, cutoff=10)
bc <- data.frame(bc)
bc$names <- rownames(bc)
bc %>% 
  arrange(desc(bc)) %>%
  slice(1:10)

##           bc   names
## 1  332.97460  Tyrion
## 2  244.63571 Samwell
## 3  226.20476 Stannis
## 4  208.62302  Robert
## 5  138.66667   Mance
## 6  119.99563   Jaime
## 7  114.33333  Sandor
## 8  111.26667     Jon
## 9   90.65000   Janos
## 10  64.59762   Aemon

Not quite what they got in the paper. Hmm.

Page rank

pageRank <- page_rank(g, damping = 0.15)$vector
head(as.matrix(sort(pageRank,decreasing = TRUE)))

##                [,1]
## Margaery 0.01282288
## Samwell  0.01238905
## Loras    0.01208873
## Drogo    0.01108128
## Qhorin   0.01097118
## Roslin   0.01088275

Again, not the same as the paper.

Adjacency matrix

p <- ggplot(storm, aes(x=Source, y=Target, fill=Weight)) +
  geom_raster() +
  theme_bw() +
  scale_x_discrete(drop = FALSE) +
  scale_y_discrete(drop = FALSE) +
  theme(
    # Rotate the x-axis lables so they are legible
    axis.text.x = element_text(angle = 270, hjust = 0),
    # Force the plot into a square aspect ratio
    aspect.ratio = 1,
    # Hide the legend (optional)
    legend.position = "none")
p

Whoa!

Reordering

# library(devtools)
# install_github("hadley/forcats")
library(forcats)

storm_ordered <- storm %>%
  left_join(ec, by = c("Source" = "names"))
storm_ordered <- storm_ordered %>%
  mutate(Source = fct_reorder(Source, ec),
         Target = fct_reorder(Target, ec))

# swap the data in the plot
p %+% storm_ordered

Change ordering to by betweenness centrality?

Light aside – Bertin matrices

In R

# install.packages("bertin",repos="http://r-forge.r-project.org")
library(bertin)
data(Hotel)
image.bertin(bertinrank(Hotel, ties.method="first"), main= "Hotel data")

plot.bertin(bertinrank(Hotel, ties.method = "first"), main= "Hotel data")

plot.bertin(Hotel, palette=c("white","black"))

On our data, doesn’t work well because it is so big!

mini_storm <- storm_ordered %>%
  filter(Source %in% ec$names[1:10],
         Target %in% ec$names[1:10]) %>%
  mutate(Source = droplevels(Source),
         Target = droplevels(Target)) %>%
  select(Source, Target, Weight)
g2 <- graph.data.frame(mini_storm)
mat <- get.adjacency(g2)
plot.bertin(bertinrank(mat, ties.method="first"))

Hmm…

Network analysis